旋转圆盘受均布压力作用时的摄动分析

THE WHITTAKER FUNCTION ASYMPTOTIC SOLUTION OF A STEADY SPINNING DISK UNDER UNIFORMLY DISTRIBUTED PRESSURE

本文对中心带轴匀速旋转圆盘在均布压力作用下的受力及变形问题进行了摄动分析,得到了受载条件为J_v^2/J_H<<1时,圆盘应力及形变的渐近解。其形变渐近解为Whittakcr函数形式。比较表明,渐近解与Chcbyshcv数值解有较好的一致性。

In this paper, the problem of a steadily spinning disk under uniformly distributed pressure is investigated by the use of perturbation method. The asymptotic solutions of stresses and deformations under the loading condition of JV2/JII< <1 is obtained. The asymptotic of deformation can be described with the Whillakcr function. Comparation shows that the asymptotic solutions are in good agreement with the Chebyshev numerical solutions.